By Ron Larson
University ALGEBRA AND CALCULUS: AN utilized technique, the latest addition to the Larson utilized math family members, permits your scholars to consider convinced relocating from collage algebra to utilized calculus. The mathematical strategies and functions are continuously offered within the similar tone and pedagogy. the mix of those topics into one textual content won't simply prevent time on your direction, however it also will store your scholars the price of an additional textbook.
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Additional resources for College Algebra and Calculus: An Applied Approach
4xϪ3 23. ͑12 Ϫ 13 ͒ Ϭ 16 Ϫ2 In Exercises 21–24, evaluate the expression for the indicated value of x. 21. ϩ 12 Ϫ 56 43. 3n 16. ͑Ϫ3 и 42͒3 19. 30 Ϭ 13 3 57 5. ͑33͒2 9. com for worked-out solutions to odd-numbered exercises. In Exercises 1–20, evaluate the expression. Write fractional answers in simplest form. 1. 22 ͑14 ͒͑5͒͑4͒ 11͑14 ͒ ϩ 54 Ϫ2 52. 5y 54. 2zy Ϫ3 4 Ϫ3 2 Ϫ2 In Exercises 55–60, write the number in scientific notation. x ϭ Ϫ7 55. Land Area of Earth: 57,300,000 square miles In Exercises 25–44, simplify the expression.
4 Ί 3 Find fourth root. и 3x ϭ Ί͑5x͒ и 3x b. Ί75x ϭ Ί25x 3 2 Find largest square factor. 2 Rewrite. ϭ 5xΊ3x, c. x ≥ 0 Find root of perfect square. ͑5x͒ ϭ Խ5xԽ ϭ 5ԽxԽ 4 Ί 4 ✓CHECKPOINT 2 Simplify Ί18x5. ■ In Example 2(c), note that the absolute value symbol is included in the 4 4 answer because Ί x ϭ x. ԽԽ Example 3 Simplifying Odd Roots и3 2 и3 3 3 a. Ί 24 ϭ Ί 8 Find largest cube factor. ϭ 3 3 Ί Rewrite. ϭ 3 3 2Ί Find root of perfect cube. иa ͒ иa 5 32a11 ϭ Ί 5 32a10 b. Ί ͑ 5 ϭΊ ϭ 2a2 5 5 a 2a2 Ί 3 54x4.
X 2 Ϫ 2x ϩ 2 Standard form x2 ϩ 2x ϩ 2 Standard form x4 Ϫ 2x 2 x 2͑x 2 Ϫ 2x ϩ 2͒ 2x3 Ϫ 4x 2 ϩ 4x 2x͑x 2 Ϫ 2x ϩ 2͒ 2x3 ϩ 2x 2 Ϫ 4x ϩ 4 2͑x 2 Ϫ 2x ϩ 2͒ x 4 ϩ 0x3 ϩ 0x 2 ϩ 0x ϩ 4 ϭ x 4 ϩ 4 So, ͑ x2 Ϫ 2x ϩ 2͒͑ x2 ϩ 2x ϩ 2͒ ϭ x4 ϩ 4. Combine like terms. 5 Polynomials and Special Products Special Products Special Products Let u and v be real numbers, variables, or algebraic expressions. Special Product Example Sum and Difference of Two Terms ͑u ϩ v͒͑u Ϫ v͒ ϭ u2 Ϫ v2 ͑x ϩ 4͒͑x Ϫ 4͒ ϭ x 2 Ϫ 16 Square of a Binomial ͑u ϩ v͒2 ϭ u2 ϩ 2uv ϩ v2 ͑x ϩ 3͒2 ϭ x 2 ϩ 6x ϩ 9 ͑u Ϫ v͒2 ϭ u2 Ϫ 2uv ϩ v2 ͑3x Ϫ 2͒2 ϭ 9x 2 Ϫ 12x ϩ 4 Cube of a Binomial ͑u ϩ v͒3 ϭ u3 ϩ 3u2v ϩ 3uv2 ϩ v3 ͑x ϩ 2͒3 ϭ x3 ϩ 6x 2 ϩ 12x ϩ 8 ͑u Ϫ v͒3 ϭ u3 Ϫ 3u2v ϩ 3uv2 Ϫ v3 ͑x Ϫ 1͒3 ϭ x3 Ϫ 3x 2 ϩ 3x Ϫ 1 Example 6 Sum and Difference of Two Terms ͑5x ϩ 9͒͑5x Ϫ 9͒ ϭ ͑5x͒2 Ϫ 92 ϭ 25x 2 Ϫ 81 ✓CHECKPOINT 6 Find the product ͑3 Ϫ x͒(3 ϩ x͒.